Testing for convergence and its pace

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productivity growth underperformance, such that a minority of economies, but a majority of the population, has seen productivity gaps decline since the 1970s. Since the GFC, this surge in productivity growth has declined in several EMDE regions. In addition, historically, sustained convergence to the frontier is rare.

In the following section, formal statistical tests of the convergence hypothesis are undertaken to assess the speed of convergence, before delving into more complex examinations of club convergence.

Countries with lower initial levels of productivity have only recently begun to outperform productivity growth in high-productivity economies on a broad basis, suggesting the presence of unconditional convergence. This has occurred in recent decades at a slow pace but does not hold over the entire sample. Convergence potential may be hindered by unfavorable characteristics in some economies that hold back productivity growth, such as poor human capital or lack of infrastructure, a phenomenon dubbed “conditional convergence” (Barro and Sala-i-Martin 1992). This section explores the pace of unconditional and conditional convergence in a more formal statistical framework.

Unconditional convergence Unconditional convergence can be assessed using a beta-convergence regression, which posits that productivity growth depends on its initial level:

yi T – yi 0 = c + βyi 0 + ϵi T , where y is the natural log of output per worker at both time T and the initial period 0 under consideration and the disturbance term ϵiT captures shocks to productivity in country i that are unrelated to convergence drivers of productivity growth. The hypothesis that β < 0 implies that lower initial productivity produces faster cumulative growth (between time 0 and time T ). When all countries have access to the same technology, those with higher marginal returns to capital—in other words, capital-scarce poorer economies—should benefit from greater capital accumulation and higher growth. The coefficient β can then be converted to an annual rate of convergence, the percent fall in the average productivity gap that is estimated to have occurred each year.7

Literature. Early estimates of β-convergence found little evidence of its existence, often instead finding that initial income was positively related to the subsequent rate of growth (Barro 1991; Baumol 1986; Dowrick 1992).8 More recent tests for unconditional

7 This is computed as (–1)∗ln(β + 1)/T, where T is the number of years under consideration, as in Barro and Sala-i-Martin (1992). 8 Barro (1991) and Barro and Sala-i-Martin (1992) apply the unconditional convergence testing procedure to U.S. states and the Organisation for Economic Co-operation and Development; Sala-i-Martin (1996) applies the procedure to Japanese prefectures and regions in five European Union countries. All studies have found little evidence of unconditional convergence.

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convergence show tentative evidence in support of the hypothesis. In tests on data from the late 1990s onward, a statistically significant negative coefficient on initial income has been found (Patel, Sandefur, and Subramanian 2018; Roy, Kessler, and Subramanian 2016). Additionally, in manufacturing, evidence in support of statistically significant unconditional convergence has also been found, although tests on an expanded set of economies have cast doubt on this finding (chapter 7; Rodrik 2013).

Results. Globally, there has been little evidence of systematic unconditional productivity convergence until last two decades, during which the negative coefficient on initial productivity becomes statistically significant (figure 4.3, panel A, and table 4C.1).9 Although statistically significant in recent decades, the estimated pace of convergence is slow, with the average economy closing just 0.5 percent of the productivity gap since 2010.10 At this rate, it would take nearly 140 years to close just half of the initial productivity gap between economies on average. In contrast, within the group of advanced economies, unconditional convergence is statistically significant and there is a clear relationship between initial labor productivity and subsequent growth (figure 4.3, panels B and C; annex 4C). Within advanced economies, labor productivity converged at a rate of 2 percent per year in the 1980s and 1990s, requiring less than 40 years to close half of the outstanding productivity gaps, although the rate of convergence has declined in recent decades as residual gaps became smaller. Even among EMDEs, a modest rate of convergence (0.3 percent) is detected over the last decade. This is evidence that, within groups with similar characteristics, economies tend to converge toward a similar productivity level.

Conditional convergence

Much of the literature has found evidence that, once country characteristics are controlled for, the coefficient on initial income becomes negative and statistically significant. Tests for conditional convergence use a similar regression specification as tests for unconditional convergence but control for country characteristics:

yit – yi 0 = c + βyi 0 + γXi + ϵi T , where Xi is a set of country characteristics. These country characteristics include the initial levels and changes in variables relating to factors such as educational attainment, trade openness, natural resources, demographics, population health, and governance.

Covariates of convergence. Controlling for the level of human capital, as measured by average years of education, has been found to result in statistically significant convergence (Barro and Lee 1994; Mankiw, Romer, and Weil 1992). Other than direct inputs into the production function, various additional factors have also been found to

9 These results are also consistent with regressions using output per capita instead of productivity. 10 Barro and Sala-i-Martin (1992) show that the speed of convergence can be calculated from a beta-test coefficient using the formula β = e -λT – 1, where λ is the annual speed of convergence and T is the number of years over which the β coefficient has been estimated.